This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A070633 #21 Dec 06 2024 16:29:56 %S A070633 2,5,2,9,2,9,2,14,2,7,2,19,2,5,2,20,2,13,2,16,2,7,2,34,2,5,2,11,2,13, %T A070633 2,27,2,5,2,31,2,5,2,30,2,13,2,14,2,7,2,51,2,7,2,11,2,15,2,19,2,7,2, %U A070633 37,2,5,2,35,2,13,2,9,2,9,2,63,2,5,2,9,2,11,2,46,2,7,2,31,2,5,2,25,2,17,2 %N A070633 a(n) is the number of k>0 such that phi(k) divides n. %C A070633 Inverse Möbius transform of A014197. - _Antti Karttunen_, Sep 10 2018 %H A070633 Antti Karttunen, <a href="/A070633/b070633.txt">Table of n, a(n) for n = 1..65537</a> %H A070633 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp). %F A070633 From _Antti Karttunen_, Sep 10 2018: (Start) %F A070633 a(n) = Sum_{d|n} A014197(d). %F A070633 a(n) >= A069932(n). %F A070633 a(A000010(n)) = A071181(n). %F A070633 (End) %o A070633 (PARI) for(n=1,120,print1(sum(i=1,100*n,if(n%eulerphi(i),0,1)),",")); %o A070633 (PARI) %o A070633 \\ In contrast to above program, this is safe in any range 1..n: %o A070633 A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))}; \\ From A014197 by _M. F. Hasler_ %o A070633 A070633(n) = sumdiv(n, d, A014197(d)); \\ _Antti Karttunen_, Sep 10 2018 %o A070633 (PARI) a(n) = sumdiv(n, d, invphiNum(d)); \\ _Amiram Eldar_, Nov 29 2024, using _Max Alekseyev_'s invphi.gp %Y A070633 Cf. A000010, A014197, A069932, A071181, A319048. %Y A070633 Row lengths of A378638. %K A070633 easy,nonn %O A070633 1,1 %A A070633 _Benoit Cloitre_, May 13 2002